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The Journal of Open Source Software

The Walrus: a library for the calculation of hafnians, Hermite polynomials and Gaussian boson sampling

Brajesh Gupt, Josh Izaac, Nicolás Quesada

Published Dec 19, 2019• 74 citations
Publisher

Abstract

Gupt et al., (2019). The Walrus: a library for the calculation of hafnians, Hermite polynomials and Gaussian boson sampling. Journal of Open Source Software, 4(44), 1705, https://doi.org/10.21105/joss.01705

DOI
10.21105/joss.01705

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Gupt et al., (2019). The Walrus: a library for the calculation of hafnians, Hermite polynomials and Gaussian boson sampling. Journal of Open Source Software, 4(44), 1705, https://doi.org/10.21105/joss.01705
Bosonic Gaussian states are ubiquitous in quantum optics and condensed matter physics. While they are efficiently handled within the Gaussian formalism, sampling requires calculating amplitudes in the boson occupation basis. This step, however, is hindered by a significant bottleneck due to the hafnian. We present an efficient algorithm that converts pure bosonic Gaussian states into matrix product states (MPSs), thereby establishing a versatile tool for probing bosonic Gaussian systems in settings where direct Gaussian-formalism-based calculations become inefficient. Our method combines a Gaussian singular value decomposition with a projected-creation-operator mapping that constructs local MPS tensors without computing hafnians. Benchmarking on covariance matrices from the Jiuzhang 2.0 and Jiuzhang 4.0 Gaussian boson sampling experiments demonstrates substantial speedups over previous tensor-network approaches in the low-entanglement regime relevant to lossy devices. The method provides a scalable classical simulation framework for bosonic Gaussian states with limited entanglement. In this regime, a target accuracy can be achieved with a bond dimension that remains computationally tractable, thereby extending the applicability of MPS-based methods to a broad range of bosonic systems.